A Course in Metric Geometry - Brossura

Burago, Dmitri; Burago, Yuri; Ivanov, Sergei

Brossura

ISBN 10: 1470468530 ISBN 13: 9781470468538

Casa editrice: Amer Mathematical Society, 2001

Riassunto

Metric geometry'' is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations.

The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Caratheodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces). The authors tend to work with ""easy-to-touch'' mathematical objects using ""easy-to-visualize'' methods.

The authors set a challenging goal of making the core parts of the book accessible to first-year graduate students. Most new concepts and methods are introduced and illustrated using simplest cases and avoiding technicalities. The book contains many exercises, which form a vital part of the exposition.

Dettagli dell'edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2001
• Lingua: Inglese
• ISBN 10: 1470468530
• ISBN 13: 9781470468538
• Rilegatura: Copertina flessibile
• Numero di pagine: 415
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile